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%I #13 Sep 08 2022 08:45:44
%S 1,44,686,-79816,-6084404,131366224,43807638856,942289429664,
%T -341856105084784,-24464562920370496,2769440413707518176,
%U 427662414707761999744,-19262659441336846931264,-7262493236035251261135616,-6531486463827292856927104,126806246226208496184168487424
%N Numerator of Hermite(n, 22/25).
%H G. C. Greubel, <a href="/A160066/b160066.txt">Table of n, a(n) for n = 0..380</a>
%F From _G. C. Greubel_, Sep 23 2018: (Start)
%F a(n) = 25^n * Hermite(n, 22/25).
%F E.g.f.: exp(44*x - 625*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 44/25, 686/625, -79816/15625, -6084404/390625, ...
%t Table[25^n*HermiteH[n, 22/25], {n, 0, 30}] (* _G. C. Greubel_, Sep 23 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 22/25)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 625*x^2))) \\ _G. C. Greubel_, Sep 23 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 23 2018
%Y Cf. A009969 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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